Robust detection and tracking algorithms for time reversal matched field processing

在时间反转匹配场处理(TR/MFP)中，传输到环境中的信号的后向散射被记录、延迟、能量归一化并重新传输到介质中。它为一维信号处理中的匹配滤波和多维信号处理中的匹配场处理(MFP)提供了一种替代传统检测器的方法。MFP的困难在于，用于对通道建模的格林函数是未知的，因此必须进行数值计算。根据其固有的性质，只要接收换能器阵列提供足够的通道采样，TR/MFP就本质上推导出通道的格林函数。TR/MFP的第二个优点在于对信道多径的有效处理。众所周知，多径对传统探测器的性能有很大的影响，被认为是一种有害的和消极的，其影响应该被最小化。TR/MFP提供了相反的机会：多路径是积极的，越多越好。虽然TR/MFP技术并不新鲜，但缺乏针对这一背景的完整的检测理论。我们的初步工作解决了这一差距，并从解析上证明了我们相信首次用TR/MFP观测到的超分辨率聚焦现象。在该建议中，我们试图进一步扩展这一分析以提供以下问题的定量答案：在经典的信号处理应用中如何使用TR/MFP，例如：(I)在丰富的杂波环境中的目标检测；(Ii)通过某种形式的空分多址(SDMA)在无线通信中的信道容量增强和均衡；以及(Iii)确定信道特性的逆断层成像问题，仅举几例。我们还将调查tr/MFP在目标定位、跟踪和识别方面有多好？Tr/mfp的基本限制是什么？为了获得准确的tr/mfp，通道必须保持多长时间不动？

In time reversal, matched field processing (TR/MFP), the backscatter of a signal transmitted into an environment is recorded, delayed, energy normalized, and retransmitted into the medium. TR/MFP offers an alternative to traditional detectors, e.g. the matched filter in one dimensional signal processing and the matched field processing (MFP) in multidimensions. The difficulty with MFP is that the Green's function used to model the channel is not known and, therefore, has to be computed numerically. By its inherent nature, TR/MFP intrinsically derives the Green's function of the channel as long as the receiving transducer array provides an adequate sampling of the channel. A second advantage of TR/MFP lies in the productive treatment of the channel multipaths. As is generally known, multipath significantly affects the performance of traditional detectors and is considered to be a detrimental and a negative whose effects should be minimized. TR/MFP presents the opposite opportunity: multipath as a positive, the more the better. Though the technique of TR/MFP is not new, but a thorough theory of detection for this setting is lacking. Our initial work addresses this gap and proves analytically, we believe for the first time, the phenomena of super resolution focusing observed with TR/MFP. In this proposal, we seek to extend this analysis further to provide quantitative answers to the following questions: How can TR/MFP be used in classical signal processing applications, such as: (i) target detection in a rich cluttering environment; (ii) channel capacity enhancement and equalization in wireless communications by some form of space division multiple access (SDMA); and (iii) inverse tomographic problems to determine channel characteristics, to name a few. We will also investigate how good TR/MFP is for target localization, tracking, and identification? What are the fundamental limits of TR/MFP? How stationary does the channel have to be for accurate TR/MFP?